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United States Patent |
6,142,681
|
Gulati
|
November 7, 2000
|
Method and apparatus for interpreting hybridized bioelectronic DNA
microarray patterns using self-scaling convergent reverberant dynamics
Abstract
A technique is described for identifying mutations, if any, present in a
biological sample, from a pre-selected set of known mutations. The method
can be applied to DNA, RNA and peptide nucleic acid (PNA) microarrays. The
method analyzes a dot spectrogram representative of quantized
hybridization activity of oligonucleotides in the sample to identify the
mutations. In accordance with the method, a resonance pattern is generated
which is representative of nonlinear resonances between a stimulus pattern
associated with the set of known mutations and the dot spectrogram. The
resonance pattern is interpreted to a yield a set of confirmed mutations
by comparing resonances found therein with predetermined resonances
expected for the selected set of mutations. In a particular example, the
resonance pattern is generated by iteratively processing the dot
spectrogram by performing a convergent reverberation to yield a resonance
pattern representative of resonances between a predetermined set of
selected Quantum Expressor Functions and the dot spectrogram until a
predetermined degree of convergence is achieved between the resonances
found in the resonance pattern and resonances expected for the set of
mutations. The resonance pattern is analyzed to a yield a set of confirmed
mutations by mapping the confirmed mutations to known diseases associated
with the pre-selected set of known mutations to identify diseases, if any,
indicated by the biological sample. By exploiting a resonant interaction,
mutation signatures may be robustly identified even in circumstances
involving low signal to noise ratios or, in some cases, negative signal to
noise ratios.
Inventors:
|
Gulati; Sandeep (La Canada, CA)
|
Assignee:
|
ViaLogy Corporation (Altadena, CA)
|
Appl. No.:
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253792 |
Filed:
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February 22, 1999 |
Current U.S. Class: |
702/19; 382/129; 435/6; 435/71.1; 435/91.1; 435/287.2; 435/288.7; 436/173; 536/25.3; 536/25.4; 702/20 |
Intern'l Class: |
G06F 015/18 |
Field of Search: |
435/6,71.1,287.2,288.7,173,91.1,291
536/25.3,25.4
934/77,78
436/173
|
References Cited
U.S. Patent Documents
5134528 | Jul., 1992 | Sato | 360/46.
|
5442593 | Aug., 1995 | Woodbury et al. | 367/135.
|
Other References
Alacid et al. Chemical Physics Letters vol. 305. 1999. pp. 258-262, May
1999.
Tsaur et al. Phys Rev. E. Stat. Phys. vol. 54 No. 5, 1996. pp. 4657-4666,
Nov. 1996.
Chandre et al. Phys. Rev. E. Stat. Phys. 1998. vol. 57. No. 2-A. pp.
1536-1543, Feb. 1998.
|
Primary Examiner: Horlick; Kenneth R.
Assistant Examiner: Taylor; Janell E.
Attorney, Agent or Firm: Pretty, Schroeder & Poplawski, P.C.
Claims
What is claimed is:
1. A method for analyzing an output pattern of a biochip to identify
mutations, if any, present in a biological sample applied to the biochip,
said method comprising the steps of:
tessellating the output pattern;
generating a stimulus pattern associated with the set of known mutations;
generating a resonance pattern representative of resonances between the
stimulus pattern and the tessellated output pattern;
interpreting the resonance pattern to yield a set of confirmed mutations by
comparing resonances found therein with predetermined resonances expected
for the selected set of mutations.
2. The method of claim 1 wherein the output pattern is derived from a
biochip microarray having a plurality of cells each having a set of
substantially identical immobilized oligonucleotides with the
oligonucleotides of each cell being substantially unique from the
oligonucleotides of every other cell.
3. The method of claim 1 wherein said step of tessellating the output
pattern comprises the step of amplifying highly local morphological
variations in the output pattern.
4. The method of claim 3 wherein the stimulus pattern is generated based
upon Quantum Expressor Functions and wherein said step of tessellating the
output pattern is performed to tessellate the output pattern to match
morphological characteristic of the Quantum Expressor Functions.
5. The method of claim 1 further including the steps of:
extracting local parametrics from the tessellated output pattern;
determining whether a degree of amplitude wandering representative of the
local parametrics is within a predetermined allowable generator function
limit; and
if not, renormalizing the tessellated output pattern to further match
spectral properties of the resonance pattern.
6. The method of claim 5 wherein said step of extracting local parametrics
from the tessellated output pattern comprises the steps of
extracting parameters representative of an integrated density of states
within each of a plurality tesselation regions within the tessellated
output pattern.
7. The method of claim 5 wherein a degree of amplitude wandering is
determined by applying a Palm distribution to develop generators for
estimating stochastic wandering.
8. The method of claim 1 further including the step of transforming the
tessellated output pattern and the stimulus pattern to a metrically
transitive random field.
9. The method of claim 8 further including the step of renormalizing the
tessellated output pattern following transformation to the metrically
transitive random field.
10. The method of claim 9 wherein said step of renormalizing is performed
to rescale the tessellated output pattern to the interval.
11. The method of claim 1 wherein the step of generating a stimulus pattern
associated with the set of known mutations comprises the steps of:
selecting a sub-set of the mutations for analysis; and
selecting a sub-set of nonlinear Quantum Expressor Functions from a set of
predetermined nonlinear Quantum Expressor Functions based upon the
selected sub-set of mutations.
12. The method of claim 11 further including the steps of:
transforming the nonlinear Quantum Expressor Functions and the tessellated
output pattern into phase space.
13. The method of claim 1 wherein the step of generating a resonance
pattern includes the step of
iteratively processing the output pattern by performing a convergent
reverberation to yield a resonance pattern representative of resonances
between a predetermined set of selected Quantum Expressor Functions and
the tessellated output pattern until a predetermined degree of convergence
is achieved between the resonances found in the resonance pattern and
resonances expected for the set of mutations.
14. The method of claim 13 wherein the step of iteratively processing the
output pattern by performing a convergent reverberation includes the step
of performing a convergent reverberant dynamics resonance analysis of the
tessellated output pattern using the resonance stimulus pattern to
identify mutations represented by the tessellated output pattern.
15. The method of claim 14 wherein the step of performing a convergent
reverberent dynamics resonance analysis includes the steps of:
a) determining resonance dynamics relaxation values based upon the
preconditioned output pattern and the resonance stimulus;
b) filtering the dynamics relaxation values using ensemble boundary and CSR
filters to yield a second set of values;
c) applying bulk property estimators to the dynamics relaxation values to
yield a third set of values;
d) evaluating the second and third sets of values to determine a degree of
resonance convergence; and
e) determining from the degree of resonance convergence whether a paralysis
of dynamics has occurred and, if so, repeating steps a)-e).
16. The method of claim 15 wherein said step of determining resonance
dynamics relaxation values based upon the preconditioned output pattern
and the resonance stimulus comprises the steps of
applying a convolutionless evolution operator to the tessellated output
pattern.
17. The method of claim 15 wherein said step of applying bulk property
estimators to the dynamics relaxation values to yield a third set of
values comprises the steps of
applying a coupling operator to which couples the dynamics relaxation
values representative of the tessellated output pattern to a nonlinear
information filter.
18. The method of claim 15 wherein said step of evaluating the second and
third sets of values to determine a degree of resonance convergence
comprises the steps of
determining whether the third set of values oscillate beyond and
predetermined threshold after a predetermined period of time and, if not,
convergence has been achieved.
19. The method of claim 18 wherein if no convergence has been achieved,
performing the additional step of increasing a timescale for determining
convergence beyond the predetermined period of time and, if convergence is
still not achieved, then generating a signal indicating that none of the
mutations of the mutation set are present in the sample.
20. The method of claim 15 wherein said step of determining whether a
paralysis of dynamics as occurred comprises the steps of evaluating a
Lindbald condition and, if the Lindbald condition has not been achieved
generating a signal indicating that paralysis of dynamics has occurred.
21. The method of claim 20 wherein, if a paralysis of dynamics has occurred
performing the additional steps of determining whether a "mutation death"
has occurred by varying a time scale for realization of the Lindbald
condition and repeating the steps beginning with determining resonance
dynamics relaxation values.
22. The method of claim 13 wherein the step of iteratively processing the
output pattern by performing a convergent reverberation also includes the
step of performing a convergent reverberant dynamics resonance analysis of
the mutations using the resonance stimulus pattern to identify diagnostic
conditions represented by the mutation.
23. The method of claim 22 wherein the step of performing a convergent
reverberant dynamics resonance analysis of the mutations using the
resonance stimulus pattern to identify diagnostic conditions represented
by the mutations includes the steps of:
a) determining resonance dynamics relaxation values based upon the
resonance stimulus and the mutations;
b) filtering the dynamics relaxation values using ensemble boundary and CSR
filters to yield a second set of values;
c) applying bulk property estimators to the dynamics relaxation values to
yield a third set of values;
d) evaluating the second and third sets of values to determine whether a
predetermined degree of resonance convergence has been achieved; and
e) if no convergence, repeat steps a)-e).
24. The method of claim 1 further including the step of
filtering the diagnostic conditions identified by the convergent
reverberant dynamics resonance analysis based upon clustering properties.
25. The method of claim 1 wherein the biological sample is selected from a
group consisting of a DNA, RNA, protein, peptide-nucleic acid (PNA) and
targeted nucleic amplification (TNA) samples.
26. The method of claim 1 further including the step of rendering a
diagnostic decision based on the diagnotic conditions identified by the
convergent reverberant dynamics resonance analysis.
27. The method of claim 26 wherein
if said diagnostic decision is negative, then determining whether any
alternatives are available; and
if no alternatives are available, selecting a new sub-set of mutations and
repeating all steps.
28. A method for preconditioning an output pattern of a biochip, said
method comprising the steps of:
a) tessellating the output pattern to match characteristics of a
predetermined stimulus pattern yielding a tessellated output pattern;
b) extracting local parametrics from the tessellated output pattern;
c) determining whether a degree of amplitude wandering representative of
the local parametrics is within a predetermined allowable generator
function limit; and
d) if not, renormalizing the tessellated output pattern to further match
spectral properties of the stimulus pattern and repeat the steps b)-d).
29. A method for performing a convergent reverberant dynamics resonance
analysis of a biochip output pattern to identify mutations represented
thereby, said method comprising the steps of:
a) determining resonance dynamics relaxation values based upon the
preconditioned output pattern and the resonance stimulus;
b) filtering the dynamics relaxation values using ensemble boundary and CSR
filters to yield a second set of values;
c) applying bulk property estimators to the dynamics relaxation values to
yield a third set of values;
d) evaluating the second and third sets of values to determine whether a
predetermined degree of resonance convergence has been achieved; and
e) determining whether a paralysis of dynamics has occurred and, if so,
repeat steps a)-e).
30. A system for analyzing an output pattern of a biochip to identify
mutations, if any, present in a biological sample applied to the biochip,
said system comprising:
a tesselation unit operative to tessellate the output pattern;
a stimulus pattern generation unit operative to generate a stimulus pattern
associated with the set of known mutations;
a resonance pattern generation unit operative to generate a resonance
pattern representative of resonances between the stimulus pattern and the
tessellated output pattern;
a resonance pattern interpretation unit operative to interpret the
resonance pattern to yield a set of confirmed mutations by comparing
resonances found therein with predetermined resonances expected for the
selected set of mutations.
31. A system for performing a convergent reverberant dynamics resonance
analysis of a biochip output pattern to identify mutations represented
thereby, said system comprising:
a determination unit operative to determine resonance dynamics relaxation
values based upon the preconditioned output pattern and the resonance
stimulus;
a fitler operative to filter the dynamics relaxation values using ensemble
boundary and CSR filters to yield a second set of values;
a estimator unit operative to apply bulk property estimators to the
dynamics relaxation values to yield a third set of values;
an evaluation unit operative to evaluate the second and third sets of
values to determine whether a predetermined degree of resonance
convergence has been achieved; and
a paralysis detection unit operative to detect whether a paralysis of
dynamics has occurred.
Description
FIELD OF THE INVENTION
The invention generally relates to techniques for analyzing biological
samples, such as DNA or RNA samples, and in particular to techniques for
analyzing the output of a hybridized biochip to which the sample has been
applied.
BACKGROUND OF THE INVENTION
A variety of techniques have been developed to analyze DNA, RNA samples or
other biological samples to identify diseases, mutations, or other
conditions present within a patient providing the sample. Such techniques
may determine, for example, whether the patient has any particular disease
such as cancer or AIDS, or has a genetic predisposition toward the
disease.
One particularly promising technique for analyzing biological samples uses
a DNA biochip (or microarray) which generates a hybridization pattern
representative of the characteristics of the DNA within the sample.
Briefly, a DNA microarray includes a rectangular array of single stranded
DNA fragments. Each element within the array includes millions of copies
of identical single stranded strips of DNA containing specific sequences
of bases. A different fragment of DNA may be provided at each different
element of the array. In other words, location (1,1) contains a different
single stranded fragment of DNA than location (1,2) which also differs
from location (1,3) etc.
A DNA sample to be analyzed is first fragmented into individual single
stranded sequences with each sequence being tagged with a fluorescent
molecule. The fragments are applied to the microarray where each fragment
bonds only with matching DNA fragments already embedded on the microarray.
Fragments which do not match any of the elements of the microarray simply
do not bond at any of the sites of the microarray and are discarded. Thus,
only those microarray locations containing fragments that match fragments
within the DNA sample will receive the fluorescent molecules. Typically, a
fluorescent light source is then applied to the microarray to generate a
fluorescent image identifying which elements of the microarray bonded with
fragments of the DNA sample and which did not. The image is then analyzed
to determine which specific DNA fragments were contained within the
original sample and to determine therefrom whether particular diseases,
mutations or other conditions are present within the DNA sample.
For example, a particular element of the microarray may be provided with
fragments of DNA representative of a particular type of cancer. If that
element of the array fluoresces under fluorescent illumination, then the
DNA of the sample contains the DNA sequence representative of that
particular type of cancer. Hence, a conclusion can be drawn that the
patient providing the sample either already has that particular type of
cancer or is perhaps predisposed towards that cancer. As can be
appreciated, by providing a wide variety of known DNA fragments on the
microarray, the resulting fluorescent image can be analyzed to identify a
wide range of conditions.
Unfortunately, under conventional techniques, the step of analyzing the
fluorescent pattern to determine the nature of any conditions
characterized by the DNA is expensive, time consuming, and somewhat
unreliable for all but a few particular conditions or diseases. FIG. 1
illustrates various conventional techniques for analyzing the flourescent
pattern. Some prior art systems utilize two or more of the techniques. It
should be noted though that many combinations of the techniques are not
provided in the prior art. Briefly, the fluorescent pattern is quantized
to yield a dot spectrogram at step 10. Any of four different techniques
are employed to identify oligonucleotides represented by the dot
spectrogram and to then identify mutations based upon the
oligonucleotides. More specifically, the dot spectrogram may be analyzed
using a trained neural network recognizer 12, a statistical decision
theory recognizer 14, a fuzzy/expectation method (EM) clustering algorithm
16 or a rule-based inferencing/truth table search 18.
The results are interpreted to yield mutations of interest at step 20. Then
the mutations are again processed using either a trained neural network
recognizer 22, a statistical decision theory recognizer 24, a fuzzy/EM
clustering algorithm 26 or a rule-based inferencing/truth table search 28.
The results are combined at step 30 to yield a diagnosis.
Finally, disease confirmation is performed at step 32 by "reduction", in
other words the disease is confirmed by probabilistic inferencing.
One major problem with many conventional techniques is that the techniques
have poor repeatability. Hence, if the same sample is analyzed twice,
different results are often obtained. Also, the results may vary from lab
to lab. Also, skilled technicians are required to operate the DNA
microarrays and to analyze the output resulting in high costs. One reason
that repeatability is poor is that the signatures within the dot
spectrogram that are representative of mutations of interest are typically
very weak and are immersed in considerable noise. Conventional techniques
are not particularly effective in extracting mutation signatures from dot
spectrograms in low signal to noise circumstances.
Accordingly, it would highly desirable to provide an improved method and
apparatus for analyzing the output of the DNA microarray to more
expediently, reliably, and inexpensively determine the presence of any
conditions within the patient providing the DNA sample. It is particularly
desirable to provide a technique that can identify mutation signatures
within dot spectrograms even in circumstance wherein the signal to noise
ration is extremely low. It is to these ends that aspects of the invention
are generally drawn.
One analysis technique for achieving the aforementioned advantages is
described in co-pending U.S. patent application 09/253,789, filed
contemporaneously herewith, entitled "Method and Apparatus for
Interpreting Hybridized Biochip Patterns Using Resonant Interactions
Employing Quantum Expressor Functions", and incorporated by reference
herein. Briefly, the method of the co-pending application operates as
follows. The method identifies mutations, if any, present in a biological
sample from a set of known mutations by analyzing a dot spectrogram
representative of quantized hybridization activity of oligonucleotides in
the biological sample to identify the mutations. A resonance pattern is
generated which is representative of resonances between a stimulus pattern
associated with the set of known mutations and the dot spectrogram. The
resonance pattern is interpreted to yield a set of confirmed mutations by
comparing resonances found therein with predetermined resonances expected
for the selected set of mutations. In a particular example described in
the co-pending application, the resonance pattern is generated by
iteratively processing the dot spectrogram by performing a convergent
reverberation to yield a resonance pattern representative of resonances
between a predetermined set of selected Quantum Expressor Functions and
the dot spectrogram until a predetermined degree of convergence is
achieved between the resonances found in the resonance pattern and
resonances expected for the set of mutations. The resonance pattern is
then analyzed to a yield a set of confirmed mutations by mapping the
confirmed mutations to known diseases associated with the pre-selected set
of known mutations to identify diseases, if any, indicated by the DNA
sample. A diagnostic confirmation is then made by taking the identified
diseases and solving in reverse for the associated Quantum Expressor
Functions and then comparing those Quantum Expressor Functions with ones
expected for the mutations associated with the identified disease to
verify correspondence. If no correspondence is found, a new sub-set of
known mutations are selected and the steps are repeated to determine
whether any of the new set of mutations are present in the sample.
By exploiting a resonant interaction, mutation signatures may be identified
within a dot spectrogram even in circumstances involving low signal to
noise ratios or, in some cases, negative signal to noise ratios. By
permitting the mutation signatures to be identified is such circumstances,
the reliability of dot spectrogram analysis is thereby greatly enhanced.
With an increase in reliability, costs associated with performing the
analysis are decreased, in part, because there is less of a requirement
for skilled technicians. Other advantages of the invention arise as well.
Although the method of the co-pending application represents a significant
advance over techniques of the prior art, room for further improvement
remains. In particular, it would be desirable to enhance the method of the
co-pending application to achieve a higher degree of repeatability.
In particular, repeatability is affected by spatio-temporal degradation of
hybridization in DNA microarrays implementing both passive and active
hybridization. In bioelectronic systems implementing passive
hybridization, sources affecting repeatability of analysis results
include:
Stochastic variability in chemical kinetics
Imnmobilized oligonucleotide damage during fabrication
Uneven kinetics during thermally facilitated fluidics reaction
Post hybridization thermal degradation. Currently biochips are
"amplification limited". This is in large part due to losses during
high-termperature hybridization downstream. During periods when the sample
temperature changes from high to low or low to high, extraneous,
undesirable reactions can occur that consume important reagents and create
unwanted and interfering chemicals. Rapid transitions ensure that the
sample spends a minimum of time at undesirable intermediate temperatures,
so that the amplified DNA product has optimum fidelity and purity. So
current methods rely on excessive amplification to compensate for these
losses.
Oligonucleotide entanglement
Environmental decoherence due to energy and radiation
Uneven fluidic catalysis
Unstable fluorescence and chemiluminiscence marker binding
Spontaneous emissions
Partial bindings
Anti-aliasing during readout and digitization
Active hybridization is degraded by
Capacitive coupling between elements of the immobilized matrix
Partial bindings due to current leakage and uneven conductance
Ultrascale quantum squeeze effects
Spontaneous emission
Nonspecific oligonucleotide trapping
Chaotic relaxation across the array
Hence, aspects of the present invention are directed, in part, to providing
enhanced repeatability of biological sample analysis despite these
factors.
SUMMARY OF THE INVENTION
In accordance with a first aspect of the invention, a method is provided
for identifying mutations, if any, present in a biological sample. The
method operates to analyze a biochip output pattern generated using the
sample to identify the mutations in the sample. In accordance with the
method the output pattern is tessellated. A stimulus pattern associated
with the set of known mutations is generated. A resonance pattern is then
generated which is representative of resonances between the stimulus
pattern and the tessellated output patterns. The resonance pattern is
interpreted to yield a set of confirmed mutations by comparing resonances
found therein with predetermined resonances expected for the selected set
of mutations.
In an exemplary embodiment, the output pattern is a dot spectrogram
representative of quantized hybridization activity of oligonucleotides in
a DNA sample. The stimulus pattern is generated based upon Quantum
Expressor Functions. The dot spectrogram is tessellated to match
morphological characteristics of the Quantum Expressor Functions and local
parametrics are extracted. The tessellated dot spectrogram and the
stimulus pattern are transformed to a metrically transitive random field
via phase shifting. The resonance pattern is generated by iteratively
processing the tessellated dot spectrogram by performing a convergent
reverberation to yield a resonance pattern representative of resonances
between the Quantum Expressor Functions and the tessellated dot
spectrogram until a predetermined degree of convergence is achieved
between the resonances found in the resonance pattern and resonances
expected for the set of mutations. The convergent reverberation includes
the step of performing a convergent reverberant dynamics resonance
analysis of the tessellated dot spectrogram using the resonance stimulus
pattern to identify mutations represented by the tessellated dot
spectrogram. The convergent reverberation also includes the step of
performing a convergent reverberant dynamics resonance analysis of the
mutations using the resonance stimulus pattern to identify diagnostic
conditions represented by the mutations.
Also in the exemplary embodiment, the convergent reverberant dynamics
resonance analyses are performed by determining resonance dynamics
relaxation values based upon the tessellated dot spectrogram and the
resonance stimulus; filtering the dynamics relaxation values using
ensemble boundary and complete spatial randomness (CSR) filters to yield a
second set of values; applying bulk property estimators to the dynamics
relaxation values to yield a third set of values; evaluating the second
and third sets of values to determine a degree of resonance convergence;
and then determining from the degree of resonance convergence whether a
paralysis of dynamics has occurred and, if so, repeating the
aforementioned steps.
In the exemplary embodiments, by tessellating the dot spectrogram to match
morphological characteristics of the Quantum Expressor Functions and by
exploiting a resonant interaction employing a resonance convergence check
which uses extracted tessellation parametric, mutation signatures may be
identified within a dot spectrogram with a high degree of repeatability.
By achieving a high degree of repeatability, the reliability of dot
spectrogram analysis is thereby greatly enhanced. With an increase in
reliability, costs associated with performing the analysis are decreased,
in part, because there is less of a requirement for skilled technicians.
Other advantages of the invention arise as well.
In accordance with a second aspect of the invention, a method is provided
for preconditioning a dot spectrogram representative of quantized
hybridization activity of oligonucleotides in a DNA samples. The method
comprises the steps of tessellating the dot spectrogram to match
characteristics of a predetermined stimulus pattern yielding a tessellated
image; extracting local parametrics from the tessellated image;
determining whether a degree of amplitude wandering representative of the
local parametrics is within a predetermined allowable generator function
limit; and if not, renormalizing the tessellated image to further match
spectral properties of the stimulus pattern and repeating the steps.
In accordance with a third aspect of the invention, a method is provided
for performing a convergent reverberant dynamics resonance analysis of a
dot spectrogram representative of quantized hybridization activity of
oligonucleotides in a DNA sample to identify mutations represented
thereby. The method comprising the steps of determining resonance dynamics
relaxation values based upon the preconditioned dot spectrogram and the
resonance stimulus; filtering the dynamics relaxation values using
ensemble boundary and CSR filters to yield a second set of values;
applying bulk property estimators to the dynamics relaxation values to
yield a third set of values; evaluating the second and third sets of
values to determine whether a predetermined degree of resonance
convergence has been achieved; and determining whether a paralysis of
dynamics has occurred and, if so, repeating the steps.
Among other applications, principles of the invention are applicable to the
analysis of various arrayed biomolecular, ionic, bioelectronic,
biochemical, optoelectronic, radio frequency (RF) and electronic
microdevices. Principles of the invention are particularly applicable to
mutation expression analysis at ultra-low concentrations using ultra-high
density passive and/or active hybridization DNA-based microarrays.
Techniques implemented in accordance with the invention are generally
independent of the physical method employed to accumulate initial
amplitude information from the bio-chip array, such as fluorescence
labeling, charge clustering, phase shift integration and tracer imaging.
Also, principles of the invention are applicable to optical,
optoelectronic, and electronic readout of hybridization amplitude
patterns. Furthermore, principles of the invention are applicable to
molecular expression analysis at all levels of abstraction: namely DNA
expression analysis, RNA expression analysis, protein interactions and
protein-DNA interactions for medical diagnosis at the molecular level.
Apparatus embodiments are also provided.
BRIEF DESCRIPTION OF THE DRAWINGS
The features, objects, and advantages of the present invention will become
more apparent from the detailed description set forth below when taken in
conjunction with the drawings in which like reference characters identify
correspondingly throughout and wherein:
FIG. 1 is a flow chart illustrating exemplary techniques for analyzing dot
spectrograms, some combinations of which are in the prior art.
FIG. 2 is a flow chart illustrating an exemplary method for analyzing the
output of a hybridized DNA microarray biochip in accordance with the
method of the co-pending application.
FIG. 3 is a flow chart illustrating exemplary enhancements to the method of
the co-pending application provided in accordance with the present
invention.
FIG. 4 is a flow chart illustrating an exemplary method for analyzing the
output of a hybridized DNA microarray in accordance with the method of the
present invention.
DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS
With reference to the remaining figures, exemplary embodiments of the
method of the co-pending application and of the present invention will now
be described. The exemplary methods will be described primarily with
respect to the analysis of mutation signatures within output patterns of
DNA biochip microarrays, but principles of the invention to the analysis
of a wide variety of other patterns as well.
Overview of Co-Pending Application
Briefly, the exemplary method of the co-pending application exploits, among
other features: (a) a novel representation, interpretation and
mathematical model for the immobilized oligonucleotide hybridization
patterns, represented via a dot spectrogram; (b) a new "active"
biomolecular target detection and discrimination method based on quantum
resonance interferometry, and (c) a new spatial hashing function that
yields accurate diagnostic assessment.
To this end the exemplary method of the co-pending application exploits a
fundamentally different computational paradigm for mutation expression
detection in pre-enhanced dot spectrogram realizations. The method is an
innovative modification to dynamically arrayed quantum stochastic
resonance (QSR) for discrete system analysis. The arraying strategy is a
function of the expression pathway of interest. The method depends on the
molecular diagnostic spectrum being addressed. Banks of coupled quantum
resonators are algorithmically designed to significantly enhance
signal-to-noise (SNR) performance and fuse multiple synthetic renormalized
dot spectrogram realizations to better detect prespecified biomolecular
expression patterns.
Moreover, the exemplary method of the co-pending application exploits an
enhancement in previous extensions to classical stochastic resonance (SR)
and array enhanced SR (AESR) in signal processing and sensor data
analysis. Stochastic resonance is a phenomenon wherein the response to a
sensor, modeled in terms of a bistable nonlinear dynamical system, is
enhanced by applying a random noise element and a periodic sinusoidal
forcing function. SR occurs when the SNR passes through a maximum as the
noise level is increased.
Thus as important aspect of the exemplary method of the co-pending
application involves the coupling of transformed and preconditioned
discrete microarray outputs to a mathematical model for a
quantum-mechanical dynamical system with specific properties. When driven
in a particular manner, the coupled system exhibits a nonlinear response
that corresponds to detection of phenomena of interest. The method
exploits modulation of observables from a "base" (canonical continuous
dynamical system), so that a selected set of spectral properties match a
similar selected spectral properties of a discrete spatial tessellation
substructure from an amplitude spectrogram derived from bioelectronic
observables. The method further exploits the concept of convolving a
discrete spatial system (derived from base mutants of interest) with a
continuous asymmetric temporal system to derive a spatiotemporal input to
further convolve with another discrete spatial projection (of an
inherently partially stabilized spatiotemporal system).
Hence key components of the exemplary biomolecular detection method of the
co-pending are: (i) selection of a basis system; (ii) generation of
designer Quantum Expressor Function (QEF) for coupling with the substrate
to be analyzed; (iii) generation of a Hamiltonian to describe relaxation
dynamics of the coupled system; (iv) modulation of resonance parameters to
enforce early resonance; (v) and exploitation of resonance suppressors to
verify detection.
Referring to FIG. 2, initially at step 100, a set of mutations of interest
are selected. The mutations, for example, may be mutations relevant to
cancer, AIDS, or other diseases or conditions. At step 101, preconditioner
transforms are generated based upon the selected set of mutations. The
preconditioner transforms are provided to convert mutation nucleotide
sequences into expected amplitude patterns in the prespecified microarray
representation, given a particular biochip layout. At step 102, Quantum
Expressor Functions are generated based upon the Hamiltonian of a
pre-selected basis system. The Quantum Expressor Functions are designed to
couple the Hamiltonian for the selected basis system to a predetermined
DNA microarray configuration to permit a resonance interaction involving
the output of the DNA microarray. Resonance stimulus is generated, at step
106, using the Quantum Expressor functions.
What has been summarized thus far are preliminary steps performed off-line
for setting up the Quantum Expressor Functions and the corresponding
resonance stimulus. These steps need be performed only once for a given
set of mutations and for a given DNA microarray configuration. Thereafter,
any number of output patterns from the DNA microarray may be processed
using the Quantum Expressor Functions to identify whether any of the
mutations of the pre-selected set of mutations are found therein.
Preferably, Quantum Expressor Functions are pre- generated for a large set
of mutations and for a large set of DNA microarray patterns such that, for
each new DNA microarray output pattern from each new patient sample, the
presence of any of the mutations can be quickly identified using the
predetermined set of Quantum Expressor Functions. In general, the
aforementioned steps need be repeated only to update the Quantum Expressor
Functions to accommodate new and different DNA microarray patterns or to
if new mutations of interest need to be considered.
At step 106, an output pattern (referred to herein as a Dot Spectrogram) is
generated using a DNA microarray for which Quantum Expressor Functions
have already been generated. At step 108, the dot spectrogram is
preconditioned to yield a dot spectrogram tesselation (DST) to permit
exploitation of a resonance between the dot spectrogram and the Quantum
Expressor Functions. The actual resonant interaction, which involves
convergent reverberations, is performed at step 110 until a pre-determined
degree of convergence is achieved. Once convergence is achieved, a
resulting resonance pattern is processed at step 112 to identify any
mutations represented thereby. As will be described below, step 112 is
rendered trivial by virtue of the aforementioned resonant interaction
which is based upon Quantum Expressor Function already correlated with the
pre-selected mutations. Hence, no complicated analysis is required to
interpret the resonance pattern to identify the mutations. Next, at step
114, the mutations are mapped to corresponding diseases and conditions to
thereby identify any diseases or conditions that the patient providing the
sample being analyzed is afflicted with. Again, this is a fairly trivial
step. Finally, at step 116, diagnostic confirmation is preformed to verify
that the diseases or conditions are present in the sample. This is
achieved by starting with the found diseases or conditions and then
performing the steps of the method in reverse.
Each of the aforementioned steps are described in detail in the co-pending
application and the detailed description thereof is not repeated herein.
Overview of the Exemplary Method of the Present Invention
The present invention is directed, in part, to improving the repeatability
of the method of the co-pending application by tessellating the dot
spectrogram so as to match morphological characteristics of the Quantum
Expressor Functions and by using extracted local parametrics as part of a
resonance convergence check during the resonance interaction. These
additional steps have the advantage of establishing uncertainty bounds
which permit method repeatability to be enhanced and quantified.
FIG. 3 illustrates enhancements to the technique of FIG. 2 provided by the
present invention along with steps of the technique of FIG. 2. The
repeated steps of FIG. 2 appearing in FIG. 3 may be the same as those of
FIG. 2 and will not be redescribed. Like reference numerals, incremented
by one hundred, are employed to represent the repeated steps.
Briefly he enhancements of the present invention entail five major steps:
Preconditioning the hybridized array output pattern (i.e. the dot
spectrogram) by a fuzzy tessellation and coupling the preconditioned
output pattern with a canonical system with aftereffect and memory
properties (step 218);
Estimation of amplitude wanderings or dispersion (step 220);
Implementation of resonance interaction by integrating partial or
subthreshold resonances using phased array enhancement operator resonance
dynamics (step 224) with additional resonances synthetically induced to
accommodate the possibility for the presence of single-point and two-point
mutations around the mutation-centered pixels; and
Resonance recombination (step 226).
A combination of one or more these enhancements are superimposed on the
techniques described in the co-pending patent application to address
specific sources of hybridization degradation, device imperfections and
protocol variability in the analysis process to thereby enhance
repeatability.
Referring now to FIG. 4, initially at step 300, a set of mutations of
interest are selected and at step 301 preconditioner transforms are
generated based upon the selected set of mutations. At step 302, Quantum
Expressor Functions are generated based upon the Hamiltonian of a
pre-selected basis system. Phase shifted resonance stimulus is generated,
at step 304, using the Quantum Expressor functions. Grouping stimulus is
also generated, at step 305.
Steps 300-305 are preferably performed off-line to set up the Quantum
Expressor Functions and the corresponding resonance stimulus and grouping
stimulus and need not be repeated other than to update the Quantum
Expressor Functions to accommodate new and different DNA microarray
patterns or if new mutations of interest need to be considered.
At step 306, a dot spectrogram is generated using a DNA microarray for
which Quantum Expressor Functions have already been generated. At step
307, the dot spectrogram is tessellated to match morphological
characteristics of the Quantum Expressor Functions yielding a dot
spectrogram tesselation (DST). At step 308, local parametrics of the
tessellated image are extracted. Then, at step 310, an amount of amplitude
wandering is determined and compared with pre-determined allowable
generator function limits. If, at step 310, the amplitude wandering is not
within the allowable generator function limits, then execution proceeds to
step 312 where the tessellated dot spectrogram to match spectral
characteristics of the Quantum Expressor Functions. Steps 308 and 310 are
repeated until the amplitude wandering is found to be within the
pre-determined limits at which point execution proceeds to block 314
wherein a resonance interaction is performed between the tessellated,
renormalized dot spectrogram and the phase shifted resonance stimulus
generated at step 304 and the group stimulus generated at step 305 to
identify any mutations represented by the dot spectrogram.
The actual resonant interaction, which involves convergent reverberations,
includes the following sub-steps also shown in FIG. 4. At step 316, a
resonance dynamics iteration is initiated which includes the use of
ensemble boundary and CSR operators (step 318) and the use of bulk
property estimators (step 320). The 20 ensemble boundary filters, CSR
filters and bulk property estimators are applied to the tessellated,
re-normalized dot spectrogram in combination with the resonance and group
stimulus. The resulting filtered dot spectrogram is then evaluated to
determine a degree of resonance convergence to one or more of the set of
predetermined mutations, at step 322. The degree of convergence is
evaluated, at step 324, against a Lindbald condition and, if the Lindbald
condition is not met, the system is deemed to be subject to paralysis of
dynamics and execution proceeds to step 326 wherein possible hixel death
is compensated for by increasing a time scale for the iteration initiated
at step 316 and then repeating the iteration.
Here it should be noted that mutation death and paralysis of dynamics are
different concepts. The mutation death check is a conditional check. If
this check shows that a resonance is not possible for a specific mutation
resonance centered (MRC)-hixel then the iteration is terminated and block
314 is exited. But failure of resonance dynamics is not sufficient to
conclude that a specific mutation is absent. Indeed, if the "hixel death"
check fails, that implies that resonance could be still obtained in a
downstream iteration.
If, at step 324, the iteration has converged and no paralysis has occurred,
then one or more mutations have been reliably identified. Execution
proceeds to block 325 wherein another resonant interaction is performed to
identify particular diseases represented by the mutations. Briefly, at
step 326, a resonance dynamics iteration is initiated which includes the
use of ensemble boundary and CSR operators (step 328) and the use of bulk
property estimators (step 330). The resulting filtered dot spectrogram is
then evaluated to determine a degree of resonance convergence, at step
332. The degree of convergence is evaluated, at step 334, against a
Lindbald condition and, if the Lindbald condition is not met, the system
is deemed to be subject to paralysis of dynamics and execution proceeds to
step 336 wherein a time scale for the iteration initiated at step 326 is
increased before the iteration is repeated. If the Lindbald condition is
met, then diseases corresponding to the mutations found using step 314
have been reliably identified.
Processing in accordance with step 335 depends on the biochip. The
flowchart of FIG. 4 illustrates a general form of the method requiring
processing during step 335. In other implementations, this step is trivial
or can be eliminated entirely. In this regard, the overall method is
implemented at two levels of abstraction, depending on how well the
disease genomics is understood. Detection of a specific mutation is
necessary and sufficient to conclude expression of a specific gene. But
the expressed gene may not be the one to conclusively identify the
disease. Then another level of abstraction is invoked wherein the method
is applied inferentially by expanding the gene expression circuit or gene
expression tree to determine if there is evidence that all expressed genes
eventually lead to one that conclusively identifies the disease. So step
335 operates on the results of step 314, such that all identified
mutations are used as an input to determine if the complete expression
pathway for leading up to the point that a disease can be concluded.
If the biochip is so designed that the mutations corresponding to all
intermediate expressed products, from any disease starting point can be
captured by resonance output of step 314, then sub-steps within step 335
and subsequent steps 340 and 342 can be circumvented. If not, clustering
step 340 and geometric hashing step 342 are provided to identify that an
expression pathway is present that trivializes the disease conclusion
=(step 344).
Once the diseases are identified, clustering properties are evaluated at
step 340 to selectively eliminate oligonucleotides representing possible
diagnoses based on morphological filtering of subthreshold resonances and
any subsequent recentering (i.e. the inverse of dispersion). Steps 314-335
produce a cluster of sub-threshold resonances. Step 340 is a
reverification such that all induced resonances are present in the target
sample and not a manifestation of multiple rescalings and synthetic SNR
enhancements.
Then a hashing projector is applied at step 342 to order the mutations. A
diagnostic decision is then rendered at step 344 by examining the order of
the mutations and comparing the mutations with a table identifying
corresponding diseases.
Thus, the output of block 314 represents all hixels that identify
complementary oligonucleotide bindings in the biological sample being
analyzed and this represent "mutations". The output of block 335 comprises
a set of expressed genes that are associated with a particular pathogenic
pathway and thus represent a preliminary "diagnosis". Further analysis of
the pathogenic pathway provides a set of possible diseases, if any. This
decomposition is motivated by scaling the computation to answer three
questions:
Does the current condition imply predisposition to a specific disease?
What is the likelihood of presence of a disease?
What is the set of all possible diseases that may be concluded from the
target sample, given a specific genomic encoding implemented by the
biochip?
In any case, if the diagnostic decision rendered at step 344 is
affirmative, then the diagnosis is output. If the diagnosis is negative
then, at step 346, a determination is made as to whether there are any
alternative mutations, not within the initial set of mutations selected at
step 300, that could be present within the sample. This determination is
made by examining a table listing all possible mutations. If there are
alternative mutations, then the process is repeated from step 300. If not,
then a signal is simply output indicating that no mutations were found in
the sample.
Now details of the steps of the new method will be provided. Details regard
steps already described in the co-pending application will not be repeated
herein.
Mutations Sets The mutation set of interest generated at step 300 is
selected by identifying oligonucleotides representative of the {Z}
mutations of interest. Each oligonucleotide is represented by .psi.(i,j)
which is given by [.alpha..sub.0 .alpha..sub.1 . . . .alpha..sub.k ],
where .alpha.={A,C,T,G} base associated with each array cell [a,b] where
10.ltoreq.k.ltoreq.25. The entire set of unique oligonucleotides denoting
mutations of interest, .increment.(l,m), is given by [.delta..sub.0
.delta..sub.1 . . . .delta..sub.k ] where .delta.={A,C,T,G} length
.vertline..increment..vertline.=length .vertline..psi..vertline., and
0<.parallel..increment.-.psi..parallel..ltoreq.k, and the designed in
.psi.(l,m) oligonucleotide sequence is a perfect complement to only
.PSI.(l,m) for all l,m.
As part of step 300, an oligonucleotide table is generated which contains
the oligonucleotide sequences associated with each mutation of interest
identified by row and column location (ij). The oligonucleotide table is
provided for subsequent use at step 312 to map locations within the dot
spectrogram wherein resonance occurs at step 310 to oligonucleotides such
that mutations present in a sample being analyzed are easily identified.
Also as part of step 300, a mutation table is generated which contains the
diseases associated with each mutation of interest. The mutation table is
provided for subsequent use at step 314 to map mutations identified at
step 312 to specific diseases or other medical conditions such that the
diseases can be easily identified.
Basis System for Quantum Expressor Functions
The selection of the basis system and the generation of the QEF's based
thereon depends, in part, and the characterisitcs of the DNA microarray.
In the exemplary embodiment, the DNA microarray is an N by M DNA chip
array wherein an element of the array is referred to herein as an "oxel":
o(i,j).
The pre-hybridization microarray (PEBC) is expressed as:
##EQU1##
where N and M refer to the linear (row and column) dimensions of the 2-D
microarray.
The numeric value associated with each oxel is given by:
##EQU2##
where [.alpha.]=[A.vertline.C.vertline.T.vertline.G] take the values
[0.vertline.1.vertline.2.vertline.3] respectively.
An element of the dot spectrogram is referred to herein as a hixel: h(ij).
A spin boson basis system is selected for use with this type of array.
Other basis system may be appropriate for either the same or other
microarray configurations.
Quantum Expressor Functions
The QEF is generated at step 302 based upon the spin Boson basis system by
first calculating the Hamiltonian for the system, calculating harmonic
amplitudes .vertline.P.sub.m .vertline. for the Hamiltonian, generating an
order function (OF), measuring entrainment entrainment states of the OF of
the ground truth and finally modulating the OF of ground truth to yield
the QEF.
The QEF's generated at step 302 are converted to a phase-space
representation. Also, if the output of the hybridization chip is not in
phase space then it is converted as well. The conversion is performed
using phase embedding operator, .GAMMA., described in the co-pending
application. Results associated with combinatorial Hopf Algebra are used
to contain amplitude dispersion due to loss of hybridization. A special
case of quantum random walk, Gelfand-Naimark Segal (GNS) construction is
used to disperse group stimulus. Note that coproduct construct of the Hopf
algebra plays the role of "sharing out" possible explanations of a fact.
The GNS dispersion of QEF is implemented using an approximation:
.PHI..sub.QEF (amp.vector)=U.sub.t aU.sub.t.sup.-1 where U.sub.t =e.sup.-it
H
where H denotes the hamiltonian for the coupling spin boson system.
Generation and Tesselation of the Dot Spectrogram
As noted a dot spectrogram is generated at step 306 for a sample from an N
by M DNA chip array wherein an element of the array is an "oxel": o(i,j).
A 6-.sigma. manufacturing process accuracy in microarray design is
assumed. Each array cell amplitude is given by .PHI.(i,j) for i: 1 to N,
and j: 1 to M. Let .PSI.(i,j) denote the a priori known oligonucleotide
given by [.alpha..sub.0 .alpha..sub.1 . . . .alpha..sub.k ], where
.alpha.={A,C,T,G} base associated with each array cell [a,b] where
10.ltoreq.k.ltoreq.25. The complimentary strand, derived from unknown
sample is denoted by .psi.(i,j).
The post-hybridization microarray is treated mathematically using the
machinery of equations with aftereffect. Each hixel given by .PHI.(i,j) is
represented as a cluster of dynamical systems of potentially [CB]
correctly bound, [UB] unbound, [PB] partially bound and [IB] incorrectly
bound. Thus [CB].sub..PHI.(i,j) +[UB].sub..PHI.(i,j) +[PB].sub..PHI.(i,j)
+[IB].sub..PHI.(i,j) =T.sub..PHI.(i,j) within 0.0001%.
The dot spectrogram .PHI.(i,j) is then tessellated to determine idealized
ensemble boundaries for forcing downstream resonant action.
Typically, in signal processing applications, high pass or band pass
spatial filtering is implemented to enhance SNR in DS matrix. Alternate
methods apply a combination of Laplacian or other edge detection filters
apply to enhance signal from arrays cells with a higher hybridization
concentration from those of the adjacent cells. These SNR enhancement
methods however work only with positive or zero-SNR. Since SNR in general
is negative in our case (ultra-low target DNA concentrations), these
methods in effect amplify noise or further blur the hixel boundaries.
Tesselation is performed by performing gradient refocusing and resealing as
described in the co-pending application. In the alternative, a Dirichlet
tessellation operator or a Delaunay triangulation operator are applied to
tessellate the dot spectrogram.
Extraction of Local Parametrics and Calculation of Amplitude Wandering
The tessellated image is treated as a metrically transitive random field.
All properties associated with a singular (deterministic), homogeneous
(i.e., stationary) field are subsumed.
The parametric of most interest is the integrated density of states, given
by
##EQU3##
where n is the number of eigenvalues to the system (random field
approximation).
This is computed for each tessellation region in the dot spectrogram.
Amplitude wandering is determined using Palm generators as described in the
co-pending patent #1. The Palm generators exploits the notion of generator
functions to capture stochastic variability in hybridization binding
efficacy. The exemplary method described herein draws upon results in
stochastic integral geometry and geometric probability theory.
"Amplitude wandering estimate" that bounds the hixel amplitude dispersion
due to total hybridization losses, is computed using Palm generators over
the globally re-scaled dot spectrogram to capture amplitude wanderings and
transitions at element, neighboring pair and local ensemble levels. Step
310 provides a measure for each mutation-recognizer centered (MRC-) hixel
that is invariant to local degradation. The measure is expressed via the
form
##EQU4##
where Z denotes the set of mutations of interest. In other words, we
determine the function f(z) under the condition that m(z) should be
invariant with respect to all dispersions .zeta.. Also, up to a constant
factor, this measure is the only one which is invariant under a group of
motions in a plane. In principle, we derive deterministic analytical
transformations on each MRC-hixel., that map error-elliptic dispersion
bound defined on .sup.2 (the two dimension Euclidean space - i.e., oxel
layout) onto measures defined on . The dispersion bound is given by the
form
Log.sub.4 (.sub.(i,j) .vertline..sup.z).
Recall that Palm distribution, .PI. of a translation (T.sub.n) invariant,
finite intensity oint process in .sup.n is defined to the conditional
distribution of the process. It is expressed in terms of a Lebesgue
factorization:
E.sub.p N*=.LAMBDA.L.sub.N X.PI.
Where .PI. and .LAMBDA. completely and uniquely determine the source
distribution P of the translation invariant point process. The term
E.sub.P N* denotes the first moment measure of the point process and
L.sub.N is a probability measure. In patent #1 we described how to compute
.PI. and .LAMBDA. which can uniquely encode the dispersion and amplitude
wandering associated with the MRC-hixel.
In this invention we relax the strong assumption that Palm generators, .PI.
and .LAMBDA., capture all sources of stochasticity in dot spectrogram
output. Since hybridization losses are affected in unknown and
unpredictable ways, we need to modify the generators as probabilistic
functions themselves. In other words the generators. are converted to
manifolds as opposed to a point function.
(.rho..sub.m(i,j), .sigma..sub.m, .eta..sub.m, .omega..sub.m) specifies a
continuous probability density function for amplitude wandering in the
m-th MRC-hixel of interest where the terms denote: oligonucleotide density
per oxel .rho..sub.m(i,j), PCR amplification protocol (.sigma..sub.m),
fluorescence binding efficiency (.eta..sub.m) and imaging performance
(.omega..sub.m). Previously we required a preset binding dispersion limit
to be apriori provided to compute A, given by the second moment to the
function at SNR =0.
##EQU5##
Nondispersive .PI. is computed using .PI.=.THETA.*P where
And .tau..sub.1 and .tau..sub.2 represent normalized hybridization
dispersion limits (typically preset to 0.1 and 0.7 respectively to assume
losses between 10% - 70% hybridization.
Preconditioned dot spectrogram is represented by .PHI.(i, j). where
function 1/(1+exp((. . . ))) was used to express the underlying known and
stationary point process.
The latter assumption is relaxed in this method and determination of
whether the amplitude wandering is within allowable generator function
limits is achieved by:
##EQU6##
where
.PI..sub.0 denotes the nondispersive generator.
.zeta..sub.1,.zeta..sub.2, . . . .zeta..sub.k provide the Laplace
characteristic functional of the Poisson random field associated with each
source of hybridization degradation. The contributions are estimated using
##EQU7##
where c is gain constant and a denotes a nonrandom matrix
a={a.sub.ij :1.ltoreq.i,j.ltoreq.d}
given by
a.sub.ij =E{a.sub.ik (.zeta.).psi..sub.kj (.zeta.)}
and are metrically transitive fields representing the unique solution of
the following variational problems:
##EQU8##
The differential operator for the metrically transitive field for convoling
the uncertainty parameters is denoted by A.sub.0. Population and solution
of the above equation requires estimates for the forward sensitivity
matrix of variables impacting hybridization degradation.
Renormalization at step 312, if necessary, is performed on the tessellated
image to further match spectral properties of the stimulus pattern The
re-normalization of the dot spectrogram is achieved by rescaling the dot
spectrogram in the interval [.pi.+.pi.]. The entire calculation proceeds
in the phase space which is why we transformed the system to the
metrically transitive random field.
Resonant Interaction to Identify Mutations
As noted, at step 314, the resonant interaction between the QEF and the
tessellated, re-normalized dot spectrogram is performed until a
pre-selected degree of convergence is achieved. Resonance dynamics
relaxation values are calculated at step 316 as follows.
A closed-form convolutionless evolution equation is given by:
##EQU9##
where both depend upon the normalized DST.sub.I (i.e., initial state) at
time .tau.- post-hybridization but pre-conditioned state. And
##EQU10##
for the hamiltonian specifying the after affect basis system dynamics.
Also,
##EQU11##
In practice a small .epsilon., typically 10.sup.6 is used.
So if theoretical convergence time is .tau..sub.0 (outer convergence cycle
time) and choosing .tau.>.tau.+.tau..sub.0, then:
##EQU12##
and .lambda. is a time-ordering operator.
The dynamics relaxation values are then filtered at step 318 using ensemble
boundary and CSR filters (higher order Poisson kernel) as follows:
##EQU13##
The bulk property estimators of step 320 are applied to the dynamics
relaxation values as follows:
##EQU14##
where t is the discretization step.
The above expression provides an estimate of when a geomteric motion
embodied by the convolutionless equation, is no longer a plausible
resonance candidate.
This is the closed form for an expression at which the coupling between DST
and the microarray is broken and a coupling with a nonlinear information
filter (NIF) is established. In essence, the system forgets any initial
correlation and tends to a Lindbald condition.
The resonance convergence is determined at step 322 as follows:
##EQU15##
The system oscillates if no convergence is reached. If increasing the
timescale x-times (.about.5) does not meet the condition, then the
mutation is deemed to be absent.
It should be noted that, unlike the technique of the co-pending
application, in the present invention the absence of resonance over a
maximum interation count does not imply absence of resonance. The reason
is that both the dot spectrogram and the QEF are dispersed, i.e., the SNR
is reduced over an individual hixel, but is in fact increased over an
ensemble. So the convergence decisions are made by cascading the inner
loop reverberations as opposed to a single reverberation. So two
timecycles are used for the convergence analysis:
(a) time cycle over which hyperfine resonances are tracked, detected and
used as a decision mechanisms to continue or stop the interation;
(b) time cycle over which the absense of mutation is actually concluded.
This is done by implementing a local maxima over output of previous step
and then reintegrating.The method essentially accumulates partial
resonances and then applies the same resonance equation to the rescaled
and renormalized partial stage.
This process can be analytically be represented as:
##EQU16##
where c.sub.1, c.sub.2 and C.sub.3 are thresholding constants that are used
to detect subthreshold resonances. Also, c.sub.1 >>c.sub.2 >>c.sub.3
>>1/[amplitude resolution].
Also .tau..sub.1 and .tau..sub.2 refer to the inner and outer integration
timescales. In an implementation they refer to the iteration conter at
which the integration loop is terminated, exceeded or exited. Typically
termination counter is set to one thousand steps with timescale of the
order of ten nanoseconds for inner step and microsecond for outer step. So
effective device convergence time is within onen hundred milliseconds for
the entire computation.
In this regard, if the Lindbald condition is not achieved and verified the
dynamics is considered paralyzed.
The paralysis of dynamics actually implies that coupling between
(a) the Quantum Expressor Function,
(b) the tessellated and normalized dot spectrogram, and
(c) the convolutionless carrier
is too weak to exhibit a nonlinear resonance. The physical interpretation
is that the coupled system exhibits "frustrated dynamics" which enhances
and impedes resonance reaction at the same time. So the actual output
takes the form of white noise over several hixels which oscillates.
The detection of oscillation occurs when the spectral radius for the
convergence criteria oscillates between limits [.epsilon..sub.1,
.epsilon..sub.2 ] and does not tend towards 0. This may be verified by
tracking the spectral radius zero crossing with respect to the lower bound
.epsilon..sub.1. If the zero crossing frequency exceeds a present number
(e.g., 10) in this implementation, the dynamics is deemed paralyzed.
If a paralysis of dynamics has occurred, a "mutation death" is evaluated as
follows. The check for MRC hixel death relates to the verification of a
suprathreshold resonance, where the resonance is defined as the integrand
of partial resonances over the entire DST structure, i.e,
##EQU17##
.A-inverted. .tau..sub.1, .tau..sub.2 .ltoreq. predefined upper limit.
Typically set to 100 for outer iteration and 1000 for inner iterations.
The time scale for realization of the Lindbald condition is changed and the
system reiterated.
Hence the final output of step 314 is all hixels that identify
complementary oligonucleotide bindings in the biological sample which are
represented computationally by the set {h.sub.k (i,j)} where {h.sub.k
(i,j)} is the corresponding oligonucleotide sequence [.alpha..sub.0
.alpha..sub.1 . . . .alpha..sub.k ] for the kth surviving hixel.
Resonant Interaction to Identify Diseases
The mutations identified using block 314 are processed using similar steps
within block 325 to identify diseases represented by the mutations. Hence
the final output of step 335 is a set of expressed genes that are
associated with a particular pathogenic pathway which is represented
computationally by the set {.psi..sup.1.sub.k (ij)} where
{.psi..sup.1.sub.k (i,j) }: [.alpha..sub.0 .alpha..sub.1 . . .
.alpha..sub.k ] for the 1-th element of the pathway capturing the k-th
disease.
For single disease analysis steps 324-334, i.e., block 335 can be omitted.
Clustering Property Check
Diseases identified using block 325 are processed at step 340 to identify
clustering properties as follows. The clustering operation is essentially
a pruning operation based on morphological filtering of subthreshold
resonances and subsequent recentering(i.e. the inverse of dispersion).
The clustering computation is based on transversal ordering (is based on
transversal numbers) of the oligonucleotide sequencing underlying the
resonance-centers for all subthreshold resonances. The concept draws from
a result in hypergraph theory. Recall that transversal of a hypergraph
H={X:E.sub.1, E.sub.2, . . . E.sub.m) is defined to be a set T .OR right.
X such that
T .andgate. E.sub.i .noteq..phi. for I=1, 2, . . . , m, where E.sub.1,
E.sub.2, . . . , E.sub.M define subgraphs.
In this method, each oligonucleotide, associated with a mutation that
survives "hixel-death" during resonant reverberation iterations, is
represented by .psi.(i,j): [.alpha..sub.0 .alpha..sub.1 . . .
.alpha..sub.k ], where .alpha.={A,C,T,G} base associated is treated as a
subgraph of the total set of unknown mutations that are actually present
in the target sample. If the surviving hixel is an ensemble than each
ensemble is treated as a subgraph with multiple nodes and several edges.
If only an individual hixel survives than it is treated as a single node
subgraph. Transversal number of a hypergraph, H, is defined as the minimum
number of vertices in a transversal. It is given by:
.tau.(H)=min .vertline.T.vertline.
The sub-steps involved in clustering are:
determine Min .Fourier.={A.sub.1,A.sub.2, . . . , A.sub.k }. where A.sub.1,
A.sub.2, . . . , A.sub.k denote the surviving resonance clusters.
Next determine the following families:
.Fourier..sub.1 ={A.sub.1 }.fwdarw.Tr{A.sub.1 }=({a}/a .di-elect
cons.A.sub.1)
.Fourier..sub.2 =.Fourier..sub.1 .orgate.{A.sub.1
}.fwdarw.Tr{.Fourier..sub.2 }=Min(Tr.Fourier..sub.1 VTr{A.sub.2 })
.Fourier..sub.3 =.Fourier..sub.2 .orgate.{A.sub.3
}.fwdarw.Tr{.Fourier..sub.3 }=Min(Tr.Fourier..sub.2 VTr{A.sub.3 })
.Fourier..sub.4 = . . .
If Min A has k members, then the algorithm constructs Tr A=Tr .sub.k in k
steps.
Hashing Projector
A hashing projector is then applied at step 342 to the output of the
clustering check. The hashing projector produces an enumeration of the
leading k oligonucleotides with the highest transveral numbers. So a set
of mutations or the corresponding expressed genes are created that have
the highest sorted transversal numbers. Typically, all members that are
seperated by a distance of, at most two, are chosen.
Diagnostic Decision
A diagnostic decision is rendered at step 344 based upon the output of the
hashing projector. The diagnostic decision is achieved using a simple
table lookup that is indexed by the results of hashing projection
computation using the aforementioned tables.
Alternatives
Alternative possible mutations are evaluated at step 346. If alternatives
are available, the alternative set of mutations of interest are loaded and
the process is repeated beginning at step 300. Hence, if the original set
of mutations from which the original set of QIF's were generated during
the off-line process of steps 301 and 302, did not include the alternative
mutations, then the off-line process is repeated with the new set of
mutations to generate new QIF's.
In the event that method yields (and it often does) multiple disease
detection hypotheses, all possible hypotheses are provided as plausible
candidates.
The technique described with respect to FIG. 4 is particularly powerful in
that it provides an enumerative solution which generally covers all
possible diagnostic candidates as opposed to only one or two, given the
best genonic understanding or mapping between expressed genes and
diseases.
Alternative Embodiments
Details regarding an implementation directed to measuring viral loads may
be found in co-pending U.S. patent application 09/253,791, also filed
contemporaneously herewith, entitled "Exponentially Convergent Therapy
Effectiveness Monitoring Using Viral Load Measurements", and also
incorporated by reference herein.
The exemplary embodiments have been primarily described with reference to
flow charts illustrating pertinent features of the embodiments. Each
method step also represents a hardware or software component for
performing the corresponding step. These components are also referred to
herein as a "means for" performing the step. It should be appreciated that
not all components of a complete implementation of a practical system are
necessarily illustrated or described in detail. Rather, only those
components necessary for a thorough understanding of the invention have
been illustrated and described in detail. Actual implementations may
contain more components or, depending upon the implementation, may contain
fewer components.
The description of the exemplary embodiments is provided to enable any
person skilled in the art to make or use the present invention. Various
modifications to these embodiments will be readily apparent to those
skilled in the art and the generic principles defined herein may be
applied to other embodiments without the use of the inventive faculty.
Thus, the invention is not intended to be limited to the embodiments shown
herein but is to be accorded the widest scope consistent with the
principles and novel features disclosed herein.
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